Every connected linear complex group Lie can be represented as a semidirect product \(B\rtimes L\) , where \(B\)  is simply connected solvable and \(L\)  is linearly complex reductive; see [1]}. Note that \(N\subset B\)  (see [2]}, where \(B\)  is called a `nucleus'). Therefore \(N^{\prime }\subset B\) . Being an integral subgroup of a simply connected solvable Lie group, \(N^{\prime }\)  is closed and simply connected [1]}. Finally, \(N^{\prime }\)  is nilpotent because it is contained in \(N\) .
